time is important.
to EJavier.
Then please explain radiation where both fields are normal to displacement but obviously do work (equally) per the photon. They do work BUT disappear because the stored energy is used . A purely static and unchanging field does no work , a changing field gives or accepts energy,- like a spring, an accellerating field gives rise to radiation , all of which you could equally say about the electrostatic field.
In a tuned circuit comprising a capacitor and an inductor which is oscillating energy is continually exchanged from one to the other in both potential and kinetic forms -- the introduction of a resistance causes an exponential decrease in oscillation as energy is used -- both fields decrease as work is done producing heat. The cap' and ind' voltages are both normal to the current( in the sinusoidal sense) so they produce no internal heat but they have changing energy, represented by the resistance heat.
But I agree that that is a non-conservative system in that heat is a random motion.
However the photon does not have to produce heat it could release (say) electrons from a metal surface exchanging energy to kinetic of the electron.
The normal force on a ramp does work -- it compresses the object which is stored energy - which can be released if the object falls off the ramp.